Understanding, Visualizability and Mathematical Explanation. In: (a cura di): Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education. p. 181-190, Lione:INRP, LYON, 2009

In this paper I focus on Mathematical Explanation in Physics and I analyse its interplay with the concepts of understanding and visualizability. Starting from a recent contextual approach to scientific understanding (De Regt & Dieks, 2005) I will try to see how an historical analysis of the formulation of a particular theorem could help to clarify the role of understanding and visualizability in mathematical explanation. My test case will be Euler’s theorem for the existence of an instantaneous axis of rotation in rigid body kinematics. In particular, I will argue that the specific concept of vector space, defining a new standard of intelligibility, offers a good perspective in order to underline the dynamical character of mathematical explanation and its essential role in mathematical education.